def create_data():
E = reference_element.DefaultTriangle()
k = 3
pts = reference_element.make_lattice(E.get_vertices(), k)
Phis = expansions.get_expansion_set(E)
phis = Phis.tabulate(k, pts)
dphis = Phis.tabulate_derivatives(k, pts)
return phis, dphis
def create_data():
E = reference_element.DefaultTriangle()
k = 3
pts = reference_element.make_lattice(E.get_vertices(), k)
Phis = expansions.get_expansion_set(E)
phis = Phis.tabulate(k, pts)
dphis = Phis.tabulate_derivatives(k, pts)
return phis, dphis
def __init__(self, ref_el, degree, shape=tuple()):
if shape == tuple():
num_components = 1
else:
flat_shape = numpy.ravel(shape)
num_components = numpy.prod(flat_shape)
num_exp_functions = expansions.polynomial_dimension(ref_el, degree)
num_members = num_components * num_exp_functions
embedded_degree = degree
expansion_set = expansions.get_expansion_set(ref_el)
sd = ref_el.get_spatial_dimension()
# set up coefficients
coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions])
coeffs = numpy.zeros(coeffs_shape, "d")
# use functional's index_iterator function
cur_bf = 0
if shape == tuple():
coeffs = numpy.eye(num_members)
else:
for idx in index_iterator(shape):
n = expansions.polynomial_dimension(ref_el, embedded_degree)
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + list(idx) + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
# construct dmats
if degree == 0:
dmats = [numpy.array([[0.0]], "d") for i in range(sd)]
else:
pts = ref_el.make_points(sd, 0, degree + sd + 1)
v = numpy.transpose(expansion_set.tabulate(degree, pts))
vinv = numpy.linalg.inv(v)
dv = expansion_set.tabulate_derivatives(degree, pts)
dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv]
for i in range(sd)]
dmats = [
numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes
]
PolynomialSet.__init__(self, ref_el, degree, embedded_degree,
expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, shape=tuple()):
if shape == tuple():
num_components = 1
else:
flat_shape = numpy.ravel(shape)
num_components = numpy.prod(flat_shape)
num_exp_functions = expansions.polynomial_dimension(ref_el, degree)
num_members = num_components * num_exp_functions
embedded_degree = degree
expansion_set = expansions.get_expansion_set(ref_el)
sd = ref_el.get_spatial_dimension()
# set up coefficients
coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions])
coeffs = numpy.zeros(coeffs_shape, "d")
# use functional's index_iterator function
cur_bf = 0
if shape == tuple():
coeffs = numpy.eye(num_members)
else:
for idx in index_iterator(shape):
n = expansions.polynomial_dimension(ref_el, embedded_degree)
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + list(idx) + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
# construct dmats
if degree == 0:
dmats = [numpy.array([[0.0]], "d") for i in range(sd)]
else:
pts = ref_el.make_points(sd, 0, degree + sd + 1)
v = numpy.transpose(expansion_set.tabulate(degree, pts))
vinv = numpy.linalg.inv(v)
dv = expansion_set.tabulate_derivatives(degree, pts)
dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv]
for i in range(sd)]
dmats = [numpy.dot(vinv, numpy.transpose(dtilde))
for dtilde in dtildes]
PolynomialSet.__init__(self, ref_el, degree, embedded_degree,
expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, size=None):
sd = ref_el.get_spatial_dimension()
if size is None:
size = sd
shape = (size, size)
num_exp_functions = expansions.polynomial_dimension(ref_el, degree)
num_components = size * (size + 1) // 2
num_members = num_components * num_exp_functions
embedded_degree = degree
expansion_set = expansions.get_expansion_set(ref_el)
# set up coefficients for symmetric tensors
coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions])
coeffs = numpy.zeros(coeffs_shape, "d")
cur_bf = 0
for [i, j] in index_iterator(shape):
n = expansions.polynomial_dimension(ref_el, embedded_degree)
if i == j:
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + [i, j] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
elif i < j:
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + [i, j] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_idx = tuple([cur_bf] + [j, i] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
# construct dmats. this is the same as ONPolynomialSet.
pts = ref_el.make_points(sd, 0, degree + sd + 1)
v = numpy.transpose(expansion_set.tabulate(degree, pts))
vinv = numpy.linalg.inv(v)
dv = expansion_set.tabulate_derivatives(degree, pts)
dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv]
for i in range(sd)]
dmats = [
numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes
]
PolynomialSet.__init__(self, ref_el, degree, embedded_degree,
expansion_set, coeffs, dmats)
def __init__(self, ref_el, degree, size=None):
sd = ref_el.get_spatial_dimension()
if size is None:
size = sd
shape = (size, size)
num_exp_functions = expansions.polynomial_dimension(ref_el, degree)
num_components = size * (size + 1) // 2
num_members = num_components * num_exp_functions
embedded_degree = degree
expansion_set = expansions.get_expansion_set(ref_el)
# set up coefficients for symmetric tensors
coeffs_shape = tuple([num_members] + list(shape) + [num_exp_functions])
coeffs = numpy.zeros(coeffs_shape, "d")
cur_bf = 0
for [i, j] in index_iterator(shape):
n = expansions.polynomial_dimension(ref_el, embedded_degree)
if i == j:
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + [i, j] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
elif i < j:
for exp_bf in range(n):
cur_idx = tuple([cur_bf] + [i, j] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_idx = tuple([cur_bf] + [j, i] + [exp_bf])
coeffs[cur_idx] = 1.0
cur_bf += 1
# construct dmats. this is the same as ONPolynomialSet.
pts = ref_el.make_points(sd, 0, degree + sd + 1)
v = numpy.transpose(expansion_set.tabulate(degree, pts))
vinv = numpy.linalg.inv(v)
dv = expansion_set.tabulate_derivatives(degree, pts)
dtildes = [[[a[1][i] for a in dvrow] for dvrow in dv]
for i in range(sd)]
dmats = [numpy.dot(vinv, numpy.transpose(dtilde)) for dtilde in dtildes]
PolynomialSet.__init__(self, ref_el, degree, embedded_degree,
expansion_set, coeffs, dmats)